Do-it-yourself Digital Swingweight Scale

(Feel free to skip this if you aren't interested in the physics and math behind swingweight.)

Almost all of this part is understanding the definition of swingweight. So let's start with that in words, then we'll go on to the physics and math.

"Balance" a golf club in a "fulcrum", or pivot, 14 inches from the butt of the club. Since the balance point of the club (also called center of gravity, CG, or center of mass) is more than 14 inches from the butt, the club will fall on its head with the grip pointing up in the air. It takes some torque to keep the club balanced in the pivot. The amount of torque needed at the pivot to balance the weight of the club is called the swingweight. It really is as simple as that! All the additional complication is in (a) definition of the unit of swingweight and (b) the technical details of accurately measuring that torque.

Let's look at a diagram of the definition. The diagram labels the important quantities in the definition, so we can go from words to equations. That's the first step in designing any measurement device. Let's call the club weight W. It acts at the CG of the club, which is L inches from the butt. If you review the meaning of torque, you will quickly see:

Swingweight = moment or torque = W (L - 14)

A swingweight scale's function is to measure the torque exerted on the fulcrum by the weight of the club. The way a conventional swingweight scale does it is to slide another weight U, between the butt and the fulcrum, until the whole assembly balances. At that point, weight U is K inches to the left of the fulcrum. We can now write the equations for equilibrium (that is, the moment of the club is balanced by the moment of weight U) as:

W (L-14) = Swingweight = U*K

Very simple algebra gives us

K =	Swingweight U

So now we know how a sliding-weight scale works. A good example, from the Maltby GolfWorks catalog, is shown in the photo. The engraved beam is calibrated in swingweight points. To measure a club, position the sliding weight U to distance K, which is proportional to swingweight.

(This is an oversimplification. We would also have to account for the moment of the frame that holds the club. We will be more careful about this below, where we analyze our digital swingweight scale.)

Units

Let's talk about the units for swingweight.

Torque is a product of a length multiplied by a force. So the units would be length times force, for instance inch-grams or inch-ounces.
Swingweight is generally expressed in "lorythmic" swingweight points. If you are building this scale, you probably know what swingweight points look like. As an example, a typical club swingweight is D-0 to D-2.

In order to measure swingweight, we need to know the conversion between length-times-force expressions of torque and lorythmic points. First let's look at how big a point is, then the origin where the points start out.

It is generally accepted that a swingweight point is 50 inch-grams. That is close, but does not correspond exactly to the original definition -- which still is the true definition. A swingweight point is actually 1.75 inch-ounces. The early pioneers of swingweight were not on the metric system. When you do the unit conversion, you find it is 49.61 inch-grams. That within 1% of 50 inch-grams. We are going to consider it 50 for much of what we do. But it will matter when we think about the origin. (Note: The critical hole position of 5.00" can be as little a 4.96". The former will give a perfect 50 inch-grams per point, and the latter a near-perfect 1.75 inch-ounces per point. Either, or anywhere in between, is quite acceptable.)

Now let's look at the origin, the "zero-point" of the lorythmic points. I have found quite a few references citing D-0 (roughly the middle of the useful range for finished clubs) as 213.5 inch-ounces. When we do the unit conversions, that comes out to 6052 inch-grams. I remember an old book by Ralph Maltby (which I can no longer find) that gives D-0 as 6050 inch-grams, which is accurate to .03%. So let's go with 6050 for purposes of our instrument.

We can even express this as a formula. If we consider D-0 to be "zero swingweight points", and higher or lower to be positive or negative points, the formula for torque (T) in inch-ounces in terms of lorythmic swingweight points (P):

T = 213.5 + 1.75 P

Converting to inch-grams, which we will find more useful with our instrument:

T = 6052 + 49.61 P

Or, to a good approximation over the range of interest:

T = 6050 + 50 P

Why so many get the origin wrong

I find surprising the number of swingweight scales that read about one point lower than detailed calculations show to be correct. I have discussed the matter with engineers at Ping and Fujikura, and now I know what happened. It boils down to their seeing the D-0 point at 6100 inch-grams, not 6050. They remain unconvinced of the error, but let me show how it occurrs.

They are fine with the historical notions that:

A swingweight point is 1.75 inch-ounces, and
D-0 is 213.5 inch-ounces.

From a simple division, D-0 is a torque of 122 swingweight points. (213.5/1.75 is 122)

Here is where they make their mistake! Since a swingweight point is 50 inch-grams, the D-0 point should be 6100 inch-grams. (122x50 is 6100)

But a swingweight point is not 50 inch-grams, it is 1.75 inch-ounces. And 1.75 inch-ounces is actually only 49.61 inch-grams, about 1% less than 50 inch-grams. If we take 122 real swingweight points, we get for D-0:

122 x 49.61 = 6052.42 inch-grams

That is a full swingweight point less than the naive estimate of 6100 for D-0.

I never understood where the error came from until I read Fujikura's patent for the design of a truly excellent digital swingweight scale. It is very advanced -- with the exception of this mistake.

(Feel free to skip this if you aren't interested in how a gram scale and a calibration procedure can measure swingweight.)

Now we know how to interpret swingweight as torque, and how to convert torque to swingweight points. Next we have to measure the torque and mechanize that conversion.

Most swingweight scales hang the club in a metal frame for measurement; that's the grey piece in the diagram. The club is still exerting a torque (the purple arrow) at the fulcrum. If we can measure the force produced by the torque at a distance M from the fulcrum, we know the torque of the combined club and metal frame. That torque is simply M times F_m.

We can do this easily enough. Place a point on the metal frame at M, and have that point rest on a gram scale. Now it is easy to compute the torque by multiplying M and F_m together. But be careful; the torque is the combined torque of the club and the frame. We will take care of this -- in fact, we will use this -- for calibration. But for now, let's just remember that the frame's torque does not change from club to club; any change in torque is due to the club's swingweight.

For convenience, we would like one swingweight point to equal an integer power of ten (e.g. - 1, 10, 100, etc) grams on the gram scale. That way, we don't need a calculator to go from a scale reading to swingweight points; we can do it in our head. A point is 50 inch-grams, so

50 = M F_m

We want F_m to be an integer power of ten for the difference of one swingweight point. That means that there are only a few choices.

F_m (grams)	M = 50/F_m (inches)
0.1	500
1	50
10	5
100	0.5

Of those choices, 5 inches is the only one I could visualize using. The others are either too small (using easily available tools, a half inch simply cannot be located within less than 1% of the position specified) or too large (where do we have 50" or 500" available on a swingweight scale?) But 5" is very comfortable for what we need to do. So we determine the size of a swingweight point with the screw at 5" from the fulcrum.

Calibration

The next thing we need to do is set where the swingweight points start. We establish that at calibration. The idea is to set the torque exerted by the metal frame itself, with no club resting in it. We choose that torque to be the equivalent of A-0 on the swingweight points range, because that is a convenient place to start our numbering.

How do we make it happen? We have to build the metal frame so it balances perfectly with an A-0 club mounted. That is, the frame by itself will have a counterclockwise torque equal to the clockwise torque of an A-0 club. If we do that, an A-0 club will make the whole thing balance.

So let's do our torque thing again. A-0 is 30 points lighter than D-0, by definition. So A-0 represents a torque of

A-0 = 6050 - (30*50) = 4550 inch-grams

We can measure 4550 inch-grams the same way we measured swingweight -- by a distance C times a force F_c, as shown in the diagram. This time we have a counter-clockwise torque, so we measure the force to the left of the fulcrum. I chose C as 9.1" so that F_c would be a nice round number, 500 grams. In practice, C is built into the instrument when you drill the hole for the round head machine screw, and you adjust F_c by loading nuts and washers on the counterweight bolt and moving them on the bolt.

I'm not sure that was the best way to choose C; it might be easier to measure and drill a hole at a nice round number of inches, and count on the digital scale for a non-round calibration force. Either way works, if you understand the math and know how to use your tools.

Do-it-yourself Digital Swingweight Scale

The physics behind it

Bill of materials

For the working parts

For the standard base

The physics and math of swingweight

Units

Why so many get the origin wrong

Physics and math behind the digital swingweight scale

Calibration